المؤلفون: René Pascal Klausen

المصدر: Journal of High Energy Physics, Vol 2022, Iss 2, Pp 1-45 (2022)

مصطلحات موضوعية: Differential and Algebraic Geometry, Scattering Amplitudes, Nuclear and particle physics. Atomic energy. Radioactivity, QC770-798

الوصف: Abstract We consider the analytic properties of Feynman integrals from the perspective of general A-discriminants and A $$ \mathcal{A} $$ -hypergeometric functions introduced by Gelfand, Kapranov and Zelevinsky (GKZ). This enables us, to give a clear and mathematically rigorous description of the singular locus, also known as Landau variety, via principal A-determinants. We also comprise a description of the various second type singularities. Moreover, by the Horn-Kapranov-parametrization we give a very efficient way to calculate a parametrization of Landau varieties. We furthermore present a new approach to study the sheet structure of multivalued Feynman integrals by the use of coamoebas.

وصف الملف: electronic resource

العلاقة: https://doaj.org/toc/1029-8479Test

الوصول الحر: https://doaj.org/article/63c0241d57a4464f9caa6c99196cb106Test

المؤلفون: René Pascal Klausen

المصدر: Journal of High Energy Physics, Vol 2020, Iss 4, Pp 1-42 (2020)

مصطلحات موضوعية: Differential and Algebraic Geometry, Scattering Amplitudes, Nuclear and particle physics. Atomic energy. Radioactivity, QC770-798

الوصف: Abstract We show that almost all Feynman integrals as well as their coefficients in a Laurent series in dimensional regularization can be written in terms of Horn hypergeometric functions. By applying the results of Gelfand-Kapranov-Zelevinsky (GKZ) we derive a formula for a class of hypergeometric series representations of Feynman integrals, which can be obtained by triangulations of the Newton polytope ∆ G corresponding to the Lee- Pomeransky polynomial G. Those series can be of higher dimension, but converge fast for convenient kinematics, which also allows numerical applications. Further, we discuss possible difficulties which can arise in a practical usage of this approach and give strategies to solve them.

وصف الملف: electronic resource

العلاقة: http://link.springer.com/article/10.1007/JHEP04Test(2020)121; https://doaj.org/toc/1029-8479Test

الوصول الحر: https://doaj.org/article/ef4f024afe4d4f338af17ce861a6074aTest

المؤلفون: René Pascal Klausen, Erik Panzer, Christian Bogner, Thomas Bitoun

المصدر: Letters in Mathematical Physics. 109(3)

مصطلحات موضوعية: High Energy Physics - Theory, Mellin transform, Polynomial, Pure mathematics, 010308 nuclear & particles physics, FOS: Physical sciences, Statistical and Nonlinear Physics, Position and momentum space, Mathematical Physics (math-ph), 01 natural sciences, Momentum, symbols.namesake, High Energy Physics - Theory (hep-th), Euler characteristic, 0103 physical sciences, D-module, symbols, Integration by parts, 010306 general physics, Mathematical Physics, Parametric statistics

الوصف: We study shift relations between Feynman integrals via the Mellin transform through parametric annihilation operators. These contain the momentum space IBP relations, which are well-known in the physics literature. Applying a result of Loeser and Sabbah, we conclude that the number of master integrals is computed by the Euler characteristic of the Lee-Pomeransky polynomial. We illustrate techniques to compute this Euler characteristic in various examples and compare it with numbers of master integrals obtained in previous works.
Comment: v2: new section 3.1 added, several misprints corrected and additional remarks

الوصول الحر: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::6a745b89b93ea9ef58a2189305a0665eTest
http://ora.ox.ac.uk/objects/uuidTest:

المؤلفون: Christian Bogner, René Pascal Klausen, Thomas Bitoun, Erik Panzer

مصطلحات موضوعية: High Energy Physics - Theory, Pure mathematics, Polynomial, Feynman integral, Dimension (graph theory), FOS: Physical sciences, Feynman graph, symbols.namesake, High Energy Physics - Theory (hep-th), Euler characteristic, symbols, Space vector, Vector space, Mathematics, Parametric statistics

الوصف: We give a brief introduction to a parametric approach for the derivation of shift relations between Feynman integrals and a result on the number of master integrals. The shift relations are obtained from parametric annihilators of the Lee-Pomeransky polynomial $\mathcal{G}$. By identification of Feynman integrals as multi-dimensional Mellin transforms, we show that this approach generates every shift relation. Feynman integrals of a given family form a vector space, whose finite dimension is naturally interpreted as the number of master integrals. This number is an Euler characteristic of the polynomial $\mathcal{G}$.
Comment: Contribution to the proceedings of Loops and Legs in Quantum Field Theory (LL2018), 29 April - 04 May 2018, St. Goar (Germany)

الوصول الحر: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::049771e7aa60d424ed58f8eef2552393Test